Hitherto, the Coulomb theory based on the theory of rupture surface has been adopted to estimate the ore pressure in a hold of an ore carrier. It introduces an approximate method for determining the stability of foundations, walls and slopes. As is indicated by experimental studies, this theory is inadequate for the present purpose.
Granular media compacted in a closed space show the elastic property accompanied with well-known characteristics as the dilatancy, and the elastic behaviors should be taken into consideration for the estimation of ore pressure.
Since Boussinesq, several authors have suggested constitutive equations for granular media by modifying Hooke's law. But these equations cannot be derived from elastic potentials, so that they cannot describe elastic deformations of granular media.
In this paper, the authors propose a nonlinear constitutive equation which shows the dilatancy phenomena. By choosing coefficients adequately, this equation is in comformity with the results of the triaxial compression test in a wide range. On the basis of this constitutive equation, stress distributions can be calculated easily by the finite element method. An experiment was performed with granular media in a cylindar subjected to non-uniform axial compression and the pressure distributions can be predicted approximately by the elastic theory.
For the precise determination of behaviors of ore, the elastic-plastic theory should be introduced, and the present constitutive equation may easily be applied with the aid of the Drucker-Prager theory of plasticity.